Nonlinear scalarizing functions in set optimization problems. (2nd September 2019)

• Record Type: Journal Article
• Authors: Han, Yu
• Is Part Of: Optimization. Volume 68:Number 9(2019)
• Page Start: 1685
• Page End: 1718
• Publication Date: 2019-09-02
• Subjects: Set optimization problem -- nonlinear scalarizing function -- Hölder continuity -- convexity; 49J53 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1602771
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we obtain Hölder continuity of the nonlinear scalarizing function for l -type less order relation, which is introduced by Hernández and Rodríguez-Marín (J. Math. Anal. Appl. 2007;325:1–18). Moreover, we introduce the nonlinear scalarizing function for u -type less order relation and establish continuity, convexity and Hölder continuity of the nonlinear scalarizing function for u -type less order relation. As applications, we firstly obtain Lipschitz continuity of solution mapping to the parametric equilibrium problems and then establish Lipschitz continuity of strongly approximate solution mappings for l -type less order relation, u -type less order relation and set less order relation to the parametric set optimization problems by using convexity and Hölder continuity of the nonlinear scalarizing functions.